Synopsis

We introduce a new high-performance nonlocal filter, NESMA, for noise reduction in multispectral (MS) MR imaging. Through extensive analysis, we show that the NESMA filter demonstrates a high degree of overall image denoising while preserving edges and small structures. We compared the performance of the NESMA filter to the multispectral nonlocal maximum likelihood (MS-NLML) filter. Although the MS-NLML filter is highly efficient, it requires extensive computational time. NESMA markedly decreases computation time while maintaining comparable levels of noise reduction and feature preservation. Finally, we show that adaptive selection of similar voxels further improves filtering quality.

Purpose

Methods

Filter Design: MS-NLML uses ML estimation (MLE) based on R similar voxels to restore the intensity of the index voxel. This process requires extensive computational time. In NESMA filtering, MLE is replaced by averaging the intensity of R voxels. In conventional NLML-based filters, R is defined using the Euclidean distance (ED).^6,7 The value of R is determined empirically and is held constant for all voxels. In this study, the similarity between the index voxel, i, and a voxel j is determined using a relative ED (RED) given by

$$RED(i,j) = \frac{\sum_{k=1}^K|S_k(i)-S_k(j)|}{\sum_{k=1}^KS_k(i)}$$

where S is the measured signal intensity and K is the total number of spectral images. RED is calculated for each voxel over a window of size M centered on i. Voxels with RED beneath a user-specified threshold are considered similar to the index voxel. This ensures that partial volume artifacts are not introduced by forced incorporation of dissimilar voxels.

Numerical analysis: 3D T₂W images of human brain were generated with representative T₂ values for white matter, gray matter, and cerebrospinal fluid chosen as 60ms, 85ms, and 180ms, respectively.^8,9 Images were generated at TEs increasing uniformly from 10 to 200ms (K=20). Rician noise was incorporated to achieve the desired SNR.⁴ Filtering performance of non-adaptive NESMA (NA-NESMA) and non-adaptive MS-NLML (NA-MS-NLML) was compared using visual inspection, absolute error (AE) maps, and the structural similarity metric (SSIM).¹⁰ R was fixed to 50 voxels. Performance of NA-NESMA and adaptive NESMA (A-NESMA) filters were compared using visual inspection and SSIM. Analyses were performed at two different SNRs. For each filter, computation time was calculated for images of different sizes. The search window size M was fixed to 25 voxels x 25 voxels x 3 voxels. For each SNR, the threshold was set to the optimal value determined using visual inspection.

Experimental analysis: 2D T₂W images were acquired from the brain of a 23-year-old female using a CPMG sequence with TE increasing uniformly from 7ms to 224ms (K=32), TR of 1200ms and voxel size of 0.67mm x 0.48mm x 2mm. Filtering parameters were similar to those used in the simulation analysis. Evaluation of filtering quality was restricted to visual inspection.

Results & Discussion

NA-MS-NLML and NA-NESMA filters provided substantial reduction of noise and detail preservation illustrated by visual inspection of filtered images, AE-maps, and SSIM (Fig.1). Further, NA-NESMA showed comparable performance to NA-MS-NLML.

Visual inspection of filtered images and SSIM evaluation shows that A-NESMA exhibits superior noise reduction as compared to NA-NESMA (Fig.2). Maps of R, the locally-determined number of similar voxels, showed large values in homogenous regions and lower values in regions with fine structures. This allows for increased noise reduction while preserving small structures.

Fig.3 demonstrates that NESMA is approximately three orders of magnitude faster than MS-NLML. For all filters, the computation time increases linearly with increasing image size. Finally, the computation time for adaptive filters is only slightly longer than that of the corresponding non-adaptive filters.

Fig.4 compares the performance of all filters. As expected, NESMA shows comparable performance to MS-NLML. Further, the adaptive filters exhibited superior performance as compared to the non-adaptive filters.

Conclusion

Acknowledgements

References

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